Answer:
The friction force and the x component for the weight should be the reaction forces that are opposite and equal to the action force, which causes the locomotive to move up the hill if the velocity of the locomotive remains constant.
Explanation:
<u>When the locomotive starts to pull the train up, appears two reaction forces opposed to the action force in the direction of the move. </u>
The first one is due to the friction between the wheels and the ground, it will be the friction force (Fr):
Fr = μ*Pₓ =μmg*sin(φ)
<em>where μ: friction dynamic coefficient, Pₓ: is the weight component in the x-axis, m: total mass = train's mass + locomotive's mass, g: gravity, and sin(φ): is the angle respect to the x-axis.</em>
And the second one is the x component for the weight (Wₓ):
Wₓ = mg*cos(φ)
<em>where cos(φ): is the angle respect to the y-axis. </em>
<em> </em>
These two forces should be the same as the action force, which causes the locomotive to move up the hill if the velocity of the locomotive remains constant.
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Answer:
The ratio of moment of inertia of larger sphere to that of smaller sphere = 4
Explanation:
The moment of inertia of solid sphere is given by I = 2/5MR² where M = mass of sphere and R = radius of sphere.
Radius of smaller sphere = D/2
Radius of larger sphere = 2D/2 = D.
Moment of inertia of smaller sphere I₁ = 2/5M × D²/4 = MD²/10
Moment of inertia of larger sphere I₂ = 2/5M × D² = 2MD²/5
The ratio of moment of inertia of larger sphere to that of smaller sphere = I₂/I₁ = 2MD²/5 ÷ MD²/10 = 10 × 2/5 = 4